Methods for determining and designing optical elements, such as lenses and mirrors, are known in the art. These methods attempt to provide accurate surfaces for uni-focal optical elements and near accurate surfaces for multi-focal optical elements. Multi-focal lenses and mirrors provide a plurality of focal points, each for a different area in the optical element.
When designing an optical element, the designer determines a list of requirements which restrict the final result. Such requirements can include a general geometry of the requested surface, a collection of optical paths which have to be implemented in the requested surface and the like. Such optical paths can be determined in theory or as measurements of the paths of light rays, which include a plurality of rays, through the optical element.
According to one method, which is known in the art, an optical surface is determined according to a preliminary given surface, which is characterized by a finite number of parameters. The method calculates an optimal choice of the parameters, thereby determining the desired optical surface. The representation of the calculated optical surface can be given by polynomials or other known special functions.
It will be appreciated by those skilled in the art that such optical surfaces are limited in that the optimization is obtained according to a limited and finite number of parameters, while the number of restrictions can be significantly larger.
G. H. Guilino, "Design Philosophy For Progressive Addition Lenses", Applied Optics, vol. 32, pp. 111-117, 1993, provides a thorough survey of the methods for design principles of multi-focal lenses.
U.S. Pat. No. 4,315,673, to Guilino et al. is directed to a progressive power ophthalmic lens. Guilino describes a specific geometry, which utilizes specific functions to achieve an optical surface with varying power.
U.S. Pat. No. 4,606,622 to Fueter et al. is directed to a multi-focal spectacle lens with a dioptric power varying progressively between different zones of vision. Fueter describes a method for determining a surface according to a plurality of points. The method defines a twice continuously differentiable surface through these points. The surface is selected so as to achieve a varying optical surface power.